It is known that the Funk transform (FT) is invertible in the class of even (symmetric) continuous functions defined on the unit 2-sphere \({\textbf{S}}^{2}\) . In this article, for the reconstruction of \(f\in { {\mathcal {C}}}^{1}({\textbf{S}}^{2})\) (can be non-even), an additional condition is found, which is a weighted Funk transform (to reconstruct an odd function), and the injectivity of the so-called two data Funk transform is considered. The transform consists of the classical FT and the weighted FT. An iterative inversion formula of the transform is presented. Such inversions have theoretical significance in convexity theory, integral geometry and spherical tomography.
